Certain types of expressions can appear asymmetric when enclosed by spanning characters. An example is fractions in which the numerator is much more complex than the denominator (or vice versa).
With the default setting SpanSymmetric->True, the size of the spanning characters above and below the axis are adjusted to be equal, giving the expression a more symmetric appearance.
For example, .
With the setting SpanSymmetric->False, the size of the spanning characters is not adjusted.